Abstract

Diffuse optical tomography (DOT) involves estimation of tissue optical properties using noninvasive boundary measurements. The image reconstruction procedure is a nonlinear, ill-posed, and ill-determined problem, so overcoming these difficulties requires regularization of the solution. While the methods developed for solving the DOT image reconstruction procedure have a long history, there is less direct evidence on the optimal regularization methods, or exploring a common theoretical framework for techniques which uses least-squares (LS) minimization. A generalized least-squares (GLS) method is discussed here, which takes into account the variances and covariances among the individual data points and optical properties in the image into a structured weight matrix. It is shown that most of the least-squares techniques applied in DOT can be considered as special cases of this more generalized LS approach. The performance of three minimization techniques using the same implementation scheme is compared using test problems with increasing noise level and increasing complexity within the imaging field. Techniques that use spatial-prior information as constraints can be also incorporated into the GLS formalism. It is also illustrated that inclusion of spatial priors reduces the image error by at least a factor of 2. The improvement of GLS minimization is even more apparent when the noise level in the data is high (as high as 10%), indicating that the benefits of this approach are important for reconstruction of data in a routine setting where the data variance can be known based upon the signal to noiseproperties of the instruments.

Received 20 December 2006Revised 29 March 2007Accepted 29 March 2007Published online 17 May 2007

Acknowledgments:

The authors are grateful to Professor Daniel R. Lynch for the useful discussions and valuable comments on this article. P.K.Y. acknowledges the DOD Breast Cancer predoctoral fellowship (BC050309). This work has been sponsored by the National Cancer Institute through Grant Nos. RO1CA78734, PO1CA80139, and DAMD17-03-1-0405.